The Factorizable Feigin-Frenkel center
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913155879272448 |
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| author | Casarin, Luca Maffei, Andrea |
| author_facet | Casarin, Luca Maffei, Andrea |
| contents | We prove a factorizable version of the Feigin-Frenkel theorem on the center of the completed enveloping algebra of the affine Kac-Moody algebra attached to a simple Lie algebra at the critical level. On any smooth curve C we consider a sheaf of complete topological Lie algebras whose fiber at any point is the usual affine algebra at the critical level and consider its sheaf of completed enveloping algebras. We show that the center of this sheaf is a factorization algebra and establish that it is canonically isomorphic, in a factorizable manner, with the factorization algebra of functions on Opers on the pointed disk for the Langlands dual Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Factorizable Feigin-Frenkel center Casarin, Luca Maffei, Andrea Representation Theory 17B65, 17B69 We prove a factorizable version of the Feigin-Frenkel theorem on the center of the completed enveloping algebra of the affine Kac-Moody algebra attached to a simple Lie algebra at the critical level. On any smooth curve C we consider a sheaf of complete topological Lie algebras whose fiber at any point is the usual affine algebra at the critical level and consider its sheaf of completed enveloping algebras. We show that the center of this sheaf is a factorization algebra and establish that it is canonically isomorphic, in a factorizable manner, with the factorization algebra of functions on Opers on the pointed disk for the Langlands dual Lie algebra. |
| title | The Factorizable Feigin-Frenkel center |
| topic | Representation Theory 17B65, 17B69 |
| url | https://arxiv.org/abs/2501.09589 |